MinT - Information on Result #2281313

Information on Result #2281313

Linear OA(8¹⁶⁰, 2097234, F₈, 23) (dual of [2097234, 2097074, 24]-code), using 1 times code embedding in larger space based on linear OA(8¹⁵⁹, 2097233, F₈, 23) (dual of [2097233, 2097074, 24]-code), using

constructionÂ X applied to C_e(22) âŠ‚ C_e(12) [i] based on
1. linear OA(8¹⁴¹, 2097152, F₈, 23) (dual of [2097152, 2097011, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 8⁷âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]
2. linear OA(8⁷⁸, 2097152, F₈, 13) (dual of [2097152, 2097074, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 8⁷âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
3. linear OA(8¹⁸, 81, F₈, 9) (dual of [81, 63, 10]-code), using
  - discarding factors / shortening the dual code based on linear OA(8¹⁸, 130, F₈, 9) (dual of [130, 112, 10]-code), using
    - trace code [i] based on linear OA(64⁹, 65, F₆₄, 9) (dual of [65, 56, 10]-code or 65-arc in PG(8,64)), using
      - extended Reedâ€“Solomon code RS_e(56,64) [i]
      - the expurgated narrow-sense BCH-code C(I) with length 65Â | 64²âˆ’1, defining interval IÂ =Â [0,4], and minimum distance dÂ â‰¥ |{−4,−3,…,4}|+1Â =Â 10 (BCH-bound) [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(8¹⁶⁰, 1048617, F₈, 2, 23) (dual of [(1048617, 2), 2097074, 24]-NRT-code)	[i]		OOA Folding
2	Linear OOA(8¹⁶⁰, 699078, F₈, 3, 23) (dual of [(699078, 3), 2097074, 24]-NRT-code)	[i]		OOA Folding